Response surface design for removal of Cr(VI) by hydrogel-supported sulfidated nano zero-valent iron (S-nZVI@H).

In this study, a new sulfidated nanoscale zero-valent iron (S-nZVI) supported on hydrogel (S-nZVI@H) was successfully synthesized for the removal of chromium (Cr) (VI) from groundwater. The surface morphology, dispersion phenomenon and functional groups of novel S-nZVI@H were characterized by scanning electron microscopy and Fourier transform infrared spectroscopy. Box-Behnken design (BBD) optimization technology based on response surface methodology (RSM) is applied to demonstrate the influence of the interaction of S-nZVI@H dose, initial Cr(VI) concentration, contact time, and initial pH with the Cr(VI) removal efficiency. The analysis of variance results (F = 118.73, P < 0.0001, R2 = 0.9916) show that the quadratic polynomial model is significant enough to reflect the close relationship between the experimental and predicted values. The predicted optimum removal conditions are: S-nZVI@H dose 9.46 g/L, initial Cr(VI) concentration 30 mg/L, contact time 40.7 min, and initial pH 5.27, and the S-nZVI@H dose is the key factor affecting the removal of Cr(VI). The predicted value (99.76%) of Cr (VI) removal efficiency is in good agreement with the experimental value (97.75%), which verifies the validity of the quadratic polynomial model. This demonstrates that RSM with appropriate BBD can be utilized to optimize the design of experiments for removal of Cr(VI).


INTRODUCTION
As a metal pollutant, Chromium (Cr) comes from industrial processes such as tanning, electroplating, metallurgy, textile (Selvi et al. 2001). Large quantities of Cr containing wastewater are drained into rivers resulting contamination of soil and groundwater. Cr usually exists in the environment in the form of trivalent chromium (Cr(III)) and hexavalent chromium (Cr(VI)) (Fendorf 1995). The toxicity of Cr(VI) is higher than that of Cr(III) mainly because of its higher solubility, fluidity and bioavailability (Kotaś& Stasicka 2000). Cr(VI) can increase the risk of cancer by entering the body through direct contact with the skin or inhalation (Gheju 2011;Zhu et al. 2017). In order to effectively control the pollution of Cr, some methods of removing Cr(VI) have been developed, including activated carbon adsorption technology (Mohan & Pittman Jr. 2006), polymer membrane filtration technology (Aroua et al. 2007), ion exchange technology (Lin & Kiang 2003), electrochemical precipitation technology (Kongsricharoern & Polprasert 1995). In order to further improve the removal efficiency of Cr(VI) and reduce the impact of the treatment processes on the environment, it is necessary to develop a green material with high removal efficiency, low cost and little secondary pollution.
In recent years, nanomaterials have been widely applied in the removal of pollutants from water (Eskandari et al. 2018;Galdames et al. 2020;Li et al. 2021;Tsade et al. 2021). Among them, nano zero-valent iron (nZVI) has been widely used in the remediation of groundwater and soil pollution due to its high specific surface area and reactivity (Zhang 2003).
Nevertheless, nZVI particles have a number of limitations that affect their reaction with contaminants: (1) nZVI easily aggregate based on the action of van der Waals force and magnetic force, and eventually reduce the migration in aquifer (Phenrat et al. 2007;Israelachvili et al. 2008;Li et al. 2017).
(2) nZVI particles with extremely high reactivity can react with other substances in the water besides the target contaminants, resulting in poor selectivity for pollutants (Cai et al. 2020;He et al. 2020). (3) When using nZVI in practice, a passivation layer can be easily to form on the surface of nZVI prohibiting Fe 0 core to react with pollutants, thus lower the reactivity (Sarathy et al. 2008). Therefore, the bare nZVI needs to be modified to improve the limitations stated above. A common approach is to load the nZVI onto inorganic carriers such as bentonite (Chen et al. 2011b), biochar (Su et al. 2016). The author applied diatomite to support nZVI to remove Cr(VI) from water achieving the better dispersion and the lower oxidation degree of nZVI with high removal rate ). In addition, the coating of polymer on the surface of nZVI is also an effective method. Chen et al. (2011a) conducted an experimental study on the removal of tetracycline from polluted water by modified nZVI with polyvinylpyrrolidone (PVP-K30). Another method for the modification of nZVI by adding transition metal to nZVI to form a bimetallic iron base. Zhu et al. (2016) reported the method of adding metal Cu to nZVI to repair Cr(VI) in groundwater.
Whereas, the higher reactivity, selectivity and lifetime of nZVI based on sulfidation have been considered as one of the promising materials (Xie & Cwiertny 2010;Fan et al. 2016aFan et al. , 2017Xu et al. 2020b). At present, there are two commonly used methods for the preparation of sulfide nanoparticles. Kim et al. (2011) used a facile one-pot synthesis process by adding a mixture of dithionite and sodium borohydride (NaBH 4 ) to a solution of ferric iron (Fe 3þ ) to synthesize Fe/FeS nanoparticles achieving high reduction rate for trichloroethylene (TCE). Another method of sulfidation is to reduce ferrous iron (Fe 2þ ) with NaBH 4 and then add Na 2 S, commonly known as the two-step synthesis method (Rajajayavel & Ghoshal 2015). Sulfurization breaks the application limit of nZVI. Fan et al. (2016a) reported that sulfidation of nZVI enhances the rate of dechlorination of TCE, indicating that the corrosion reaction with water of nZVI is suppressed. In view of improving lifetime of S-nZVI, Xie & Cwiertny (2010) proposed that the reduction ability of aged nZVI could be restored by using dithionite as a reducing agent to sulfurize the nZVI so as to prolong its lifetime. In addition, sulfidation significant increases the crystal domain size and lattice spacing of iron. The larger lattice constant is benefit for the electron transfer, thus improving the reactivity and selectivity for the reduction of contaminants (Xu et al. 2020a). These achievements are impressive and indicate that S-nZVI has great potential for the removal of pollutants from water (Su et al. 2015a;Li et al. 2016Li et al. , 2017aLi et al. , 2018b. In order to improve the aggregation phenomenon and anti-oxidation property of S-nZVI, it is an effective choice to use porous material as the supported carrier of nanoparticles. Chen et al. (2020) proposed to remove TCE from groundwater by loading S-nZVI on biochar (BC). The promotion of removal and degradation of TCE was benefit from the high adsorption capacity of BC and the high reduction capacity of S-nZVI. Some other researchers have also applied inorganic porous material and to support S-nZVI for removal of heavy metal (Su et al. 2015b;Qu et al. 2021) and toxic dye (Yang et al. 2018). Based on its strong response to environmental stimulation, biocompatibility, swelling property, and elasticity, hydrogels have been used in drug transportation, eyeglasses manufacturing, biosensor development, artificial muscle and other aspects (Manetti et al. 2002;Sahiner et al. 2006;Satarkar & Zach Hilt 2008;Fuhrer et al. 2009;Jain et al. 2017). In this study, organic hydrogels with non-toxic, environmentally friendly, cheap and porous properties were selected as the carrier of S-nZVI. Hydrogel has super function of absorbing contaminants ( Jin et al. 2009;Sahiner & Ilgin 2010) due to the threedimensional (3D) network formed by cross-linking of polymer chains. In addition, hydrogels also have hydrophilic functional groups such as COOH, OH, CONH 2 , and NH 2 in the structure, where negatively charged COOH can be combined with positively charged metal ions (Cu 2þ and Fe 2þ ) in aqueous solution by electrostatic force (Chauhan et al. 2006;Sahiner et al. 2010a). Consequently, hydrogels can be used as reaction containers for in-situ reduction of metal nanoparticles (Sahiner 2006;Sahiner et al. 2010b). The metal nanoparticles are uniformly dispersed in the hydrogel network system, thus avoiding the serious aggregation of nanoparticles. Furthermore, hydrogels can be used as a protective structure to reduce the oxidation degree of nanoparticles to a certain extent. Obviously, it is worth expecting to combine S-nZVI with hydrogel (S-nZVI@H) to form a novel material, so as to fully amplify the super reduction ability of S-nZVI particles, and then repair the pollution of Cr(VI) in groundwater.
Response surface methodology (RSM) is a design method that combines mathematics and statistics to establish polynomial models based on experimental data (Bezerra et al. 2008). After determining independent variables, designing experiments, data statistics and model validation, the goal of determining the optimal independent variable conditions is achieved. Box-Behnken design (BBD) is one of the optimization analysis methods in the quadratic response surface design method, which can show the influence of interaction between multiple variables on the response value and avoid the combination of all variables in extreme circumstances (Ferreira et al. 2007;Bezerra et al. 2008).
In this study, nZVI@H and S-nZVI@H were synthesized and characterized for the removal of Cr(VI). Scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) were applied to survey the surface morphology, dispersion phenomenon, and structure of original hydrogels, nZVI, nZVI@H, and S-nZVI@H. Comparison experiments were performed to research the removal efficiency of nZVI@H and S-nZVI@H. Considering the removal efficiency, S-nZVI@H was selected as the material for the response surface experiment design. The S-nZVI@H dose, initial Cr(VI) concentration, contact time, and initial pH were taken as independent variables to explore the influence of the interaction of four independent variables on the Cr(VI) removal efficiency. so as to acquire the optimal conditions for removal Cr(VI).

Materials
Analytical pure levels of chemicals and reagents were used in this study. Ferrous sulfate (FeSO 4 ·7H 2 O), sodium hydrosulfite (Na 2 S 2 O 4 ), and sodium borohydride (NaBH 4 ) were purchased from Tianjin Fuchen Chemical Reagent Factory (Tianjin, China). The solution required in the experiment was mixed with deionized water. HCl (0.1 mol/L) and NaOH (0.1 mol/L) were used to adjust the pH of the solution.

Preparation of S-nZVI@H
The prepared sodium polyacrylate and polyacrylamide were copolymerized in a constant temperature water bath and dried to obtain the PANa-PAM hydrogel used in this study. The S-nZVI was prepared by one-pot method initiated by (Kim et al. 2011). The S-nZVI@H composites were prepared by supporting S-nZVI on hydrogel. Firstly, hydrogel globules were dipped in ferrous sulfate solution (0.1 mol/L) for 24 hours. After soaking, the hydrogel globules were filtered with deionized water for three times to remove Fe 2þ on its surface. Then a three-necked flask was prepared to fill the soaked hydrogel globules, which were immersed in deionized water. S-nZVI@H were prepared by liquid phase reduction method. For the preparation of the reaction solution, NaBH 4 (1 mol/L) and Na 2 S 2 O 4 (0.1 mol/L) were put into the 250 mL conical flask and dissolved by stirring with 200 mL of deionized water. The reductant solution was injected into the three-neck flask at 28 L/min through a peristaltic pump in nitrogen atmosphere and stirred at 90 r/min for one hour. The reaction process of zero-valent iron (Fe 0 ) is exhibited in Equation (1): The formation of FeS occurs during the reduction of Fe 2þ , which was shown in Equations (2)-(5): The acquired S-nZVI@H composites were immersed in deionized water for 2 h in the presence of nitrogen to remove the residual NaBH 4 and Na 2 S 2 O 4. Finally, the fresh S-nZVI@H were dried by Freeze Drier (FD-1 A-50) for 24 hours.

Cr(VI) removal batch experiments
Removal experiments were deployed using 250 mL conical flask containing 200 mL Cr(VI) solution at 25°C. Different masses of K 2 Cr 2 O 7 were taken and dissolved in deionized water with different pH values. Afterwards, the S-nZVI@H of various dosage were added inside conical flask with a certain concentration of Cr(VI) solution, which were shaken evenly by a constant temperature shaker (DSHZ-33A) at 180 rpm for 25°C. Solution was withdrawn from injection syringe at certain reaction time intervals. The concentration of the reaction solution was determined at 540 nm by a UV-visible spectrophometer (2082SUV/VIS) using diphenylcarboxyl dihydrazine spectrophotometry method. Finally, the efficiency of Cr(VI) removal was calculate using Equation (6): In which C 0 is the initial concentrations (mol/L) of Cr(VI) and C is the concentrations (mol/L) after removal at a certain time.

Experimental design
In the content of this study, Box-Behnken Design (BBD) was applied to conduct the RSM to acquire the optimal conditions for removal and the most significant factor affecting the removal. Practical optimization steps and the main content of this work are as follows: (1) determination of independent variables with relatively significant influence. (2) batch experiments of removal at determined conditions. (3) the mathematical model was established by quadratic polynomial function fitting with experimental data. (4) figure out the optimal conditions for removal and the independent variable of most significant effect. (5) validation experiment was conducted under the given optimal removal conditions obtained from the previous fitting procedure. The S-nZVI@H dose (A), the initial Cr(VI) concentration (B), contact time (C), and initial pH (D) are selected as independent variables. The Cr(VI) removal efficiency is set to the predicted response value. The influence of the interaction of four independent variables and one response value is described by using the quadratic polynomial model (Equation (7)).
where R is the predicted response value of Cr(VI) removal, b 0 is the intercept value; b 1 ∼ b 4 are the linear coefficients; b 12 ∼ b 14 , b 23 ∼ b 24 and b 34 are the cross-product coefficients; b 11 ∼ b 44 are the quadratic coefficients; A, B, C and D are the code forms of the input variables (Gopinath et al. 2010).
In this study, the experimental data are coded and analyzed with Design-Expert 8.0.6 Trial. Four independent variables and levels of them are listed in Table 1. Additionally, the experimental design procedure and results of Cr(VI) removal are shown in Table 2. Moreover, 29 groups of experiments are designed which included five parallel experiments. The method of variance (ANOVA) is used to determine the fitting degree between the values obtained from the experiment and the predicted response values calculated by the regression mode (Silveira et al. 2017). The statistical significance is evaluated by the coefficient of determination R 2 (Khosravi & Arabi 2016).

RESULTS AND DISUSSION
Characterizations of the hydrogel, nZVI, nZVI@H and S-nZVI@H FTIR was used to reveal the chemical functional groups of PANa-PAM hydrogel, nZVI, nZVI@H, and S-nZVI@H ( Figure 1). The broad peak around 3,420 cm À1 is assigned to hydroxyl groups (Dong et al. 2018). The peak near 2,370 cm À1 is the  (Dong et al. 2018). The peak at 1,310 cm À1 is attributed to C-C stretching (Tang et al. 2008). The absorption peak occurred at 1,670 cm À1 , 1,570 cm À1 and 1,390 cm À1 are assigned to C ¼ O stretching, the N-H bending and -C-N-deformation of the -CONH 2 group in the hydrogel, respectively (Tang et al. 2008;Dong et al. 2019). Likewise, the absorption peak at around 1,420 cm À1 is attributed to the symmetric stretching vibration of the -COO À anions in the hydrogel (Tang et al. 2008). These absorption peaks of the hydrogel described above also present in nZVI@H and S-nZVI@H, indicating that nZVI and S-nZVI have been successfully supported by hydrogels. Besides, the adsorption peak at about 470 cm À1 corresponds to Fe-O stretches due to the oxidation of nZVI in the air (Zhang et al. 2011). Occurrence of less obvious Fe-O stretches in nZVI@H and S-nZVI@H may be caused by the fact that the degree of oxidation of these two materials is modestly inhibited. The new band spectrum at 1,100 cm À1 and 830 cm À1 of S-nZVI@H compared with the infrared images of nZVI@H further indicates that nZVI has been successfully sulfidation (Chernyshova 2003;Reyes-Bozo et al. 2015). SEM was applied to elucidate the surface morphology and structure of PANa-PAM hydrogel, nZVI, nZVI@H, and S-nZVI@H. The porous network structure of PANa-PAM hydrogel is clearly observed in Figure 2(a). The spherical structure Uncorrected Proof of bare nZVI is shown in Figure 2(b). It can be observed that the diameter of nZVI particles is less than 100 nm with aggregation. The surface morphologies of nZVI@H and S-nZVI@H are demonstrated in Figure 2(c) and 2(d), respectively. The porous structure of the supported hydrogel retains with a rougher surface. Both nZVI and S-nZVI particles are successfully loaded in the hydrogel as small bulges in granular form and their dispersion performance is relatively better than that of bare nZVI. The unique 3D structure of PANa-PAM hydrogel can effectively inhibit the aggregation of nanoparticles. Particularly, it is obvious from Figure 2(d) that the size of S-nZVI particles distributed in porous hydrogel is larger with a better uniform distribution, which may be due to the minimization of aggregation by electrostatic repulsion and steric hindrance in the case of sulfidation.

Comparison of removal of Cr(VI) between nZVI@H and S-nZVI@H
According to previous studies on S-nZVI, the reactivity and selectivity of S-nZVI with pollutants are greatly enhanced compared with bare nZVI (Fan et al. 2016b(Fan et al. , 2017. A comparative experiment was conducted to further explore Cr(VI) removal efficiency of S-nZVI@H and nZVI@H under certain experimental conditions (initial Cr(VI) concentration of 20 mg/L, pH at 6, nZVI@H and S-nZVI@H dosage of 6 g/L and temperature of 25°C). Figure 3 shows that the removal efficiency of nZVI@H and S-nZVI@H increases rapidly in the first 30 minutes. After 60 minutes, the Cr(VI) removal efficiencies of both of them reach more than 90%. Especially, the removal efficiency of S-nZVI@H is 24.89% higher than that of nZVI@H at the 5th minute. During the reaction of Cr(VI) and S-nZVI@H, the sulfur species FeS enhances the transfer of electrons from the core to the surface of nZVI, thus increasing the probability of Cr(VI) reduction (Li et al. 2018a;Brumovský et al. 2021). Brumovský et al. (2021) verified that S-nZVI was more effective in removing Cr(VI) than nZVI in laboratory conditions. Additionally, Su et al. (2015a) reported that S-nZVI had higher surface area rather than bare nZVI generating more metal ion adsorption binding sites. Accordingly, the reason why S-nZVI@H can remove Cr(VI) more quickly and effectively compared with nZVI@H is that sulfidation can improve the dispersity of nZVI and selectivity of nZVI to Cr(VI). Specifically, sulfidation of nZVI reduces the magnetic interaction between nZVI nanoparticles by the formation of iron-sulfide compound, as a result of ameliorating the aggregation. Moreover, the outer layer created by sulfidation decreases the direct reaction of nZVI with water, thus improving the electron selectivity for the reduction of Cr(VI), so as to extending its reactive lifetime. Particularly, PANa-PAM hydrogel provides a protective layer for the passivation of S-nZVI, and makes S-nZVI more evenly distributed in the hydrogel network, thus improving the reduction effectivity of Cr(VI). Therefore, the removal of Cr(VI) by S-nZVI@H is further analyzed by RSM. þ 3:97CD À 19:80A 2 À 1:02B 2 À 16:78C 2 À 4:82D 2 The predicted response value of Cr(VI) removal is calculated according to Equation (8), and the calculated results are presented in Table 2. In order to understand the fitting effect between the predicted response values and the experimental values in detail, the fitting curve between them was obtained by RSM. Figure 4 shows that data points are distributed at both ends of the straight line and most of them are distributed on the straight line. The coefficient of determination (R 2 ) of the linear equation is 0.9916 which indicate the quadratic polynomial model has better fitting degree and higher accuracy. The root mean squares error (RMSE ¼ 2.32) and the absolute average deviation (AAD ¼ 5.39) of the model were calculated according to Equations (9) and (10). RMSE and AAD are parameters that evaluate the difference (Liu et al. 2009) and the degree of regression (Zheng et al. 2020) between the predicted response values of the model and the experimental values, respectively.
where n is the number of experiments, y b is the predicted response value and y a is the experimental value (Sohrabi et al. 2014). Analysis of variance (ANOVA) is used to evaluate the regression significance of quadratic polynomial model and the nonsignificance of inadequate fitting. Besides, the fitting degree of the model is evaluated by F-value, P-value, lack-of-fit and R 2 , so as to verify the quality and reliability of the model (Mohammadi et al. 2017). With the larger F-value and the smaller P-value, the significance of the model is higher. The model is logical when the F-value of the model is greater than the critical F-value. The critical F-value is calculated according to F 0:05, df, (nÀdfþ1): F 0:05,14,14 is 2.484 referring to F test threshold table. The critical  Uncorrected Proof F-value is less than the calculated F-value. As can be seen from Table 3, F-value of the model is equal to 118.73 and P-value is less than 0.05, which indicate that the model is significantly effective (Mansouriieh et al. 2019). Among the four model items A, B, C and D, item A has the largest F-value, indicating that the dosage of S-nZVI@H has a significant effect on the predicted response value of the model, which can be used as the key factor for Cr(VI) removal. Furthermore, F-value of D is smaller than that of the other three items, indicating that the initial pH value of solution has little influence on the predicted response value of the model. The F-value of lack-of-fit is equal to 2.92, which is not obvious, indicating that it is not important in model fitting compared with pure error. Meanwhile, due to noise, there is 15.64% probability of F-value missing. The degree of dispersion of data points is reflected by the square root of the variance (Std.Dev (3.33)) and the ratio of standard deviation to mean value (C.V (5.17)). A smaller value of C.V indicates that the data points and mean value are approaching, which describe the reliability of the model is higher. The predicted residual sum of squares (PRESS) is used to measure the responsive ability of the model to predict experiment, and the model is ideal when the value of PRESS is small (Sohrabi et al. 2014). Adeq Precision represents the signal to noise ratio (SNR). According to Table 3, the SNR is equal to 39.096 and the value is greater than 4, indicating that this model is reliable to predict experiments (Beg et al. 2003;Sohrabi et al. 2014). R 2 (Equation (11)) is the ratio of the sum of squares of the model (SS Model ) to the sum of squares of the total (SS Total ), which can be used to evaluate the degree of fitting between experimental values and predicted values of the model (Mansouriieh et al. 2019). Especially, the R 2 should be within the range from zero to one (0 R 2 1). The closer R 2 is to 1, the better the model fitting effect is.

Uncorrected Proof
The calculated R 2 is 0.9916 (Table 3), which indicates that there is a 99.16% probability that the predicted value of the model has a linear relationship with the experimental value. Adjusted R-squared (0.9833) and predicted R-squared (0.9561) of the regression line are presented in Table 3. Obviously, these two values are close to each other and can well express the predicted response value of the model under the condition of adjusted R-squared.
The residual graph is drawn to verify whether the residual of the model has the characteristics of normality, independence and constancy (Un et al. 2014). Figure 5(a) is residual normal possibility diagram, which indicates that the distribution of residuals conforms to the characteristics of Gaussian distribution, thus verifying the normal distribution characteristics of residuals. The chronological diagram of residuals is shown in Figure 5(b). Residual values are distributed between À3.93 and 3.93 with irregular distribution characteristics, which shows the independence of residuals. If the model is correct and reliable, the residual does not exhibit a special structure and does not have a relationship with other variables (Mansouriieh et al. 2019). Figure 5(c) is residual graph based on predicted values. The distribution of residuals within a certain range is also irregular, which shows the constancy of residuals. The smaller the residual is when the residual data points are close to the zero line. The more residual data points close to the zero line, the better the fitting degree between the predicted value and the experimental value. These three residual diagrams show that the quadratic polynomial model established by RSM has certain reliability and can effectively predict the experimental results. Based on the quadratic polynomial model, the 3D response surface map can visualize the relationship between the interaction of the two independent variables and the Cr(VI) removal efficiency while keeping the other two variables fixed. Figure 6 shows the effects of the interaction between two of the four independent variables (S-nZVI@H dose (A), initial Cr(VI) concentration (B), contact time (C), and initial pH (D)) on the removal efficiency of Cr(VI) by S-nZVI@H. In each response surface diagram, under certain two variables, the highest point of the surface is the best reaction condition under which the maximum removal efficiency can be obtained.

Uncorrected Proof
The interactive impact of the combination of S-nZVI@H dose and initial Cr(VI) concentration on Cr(VI) removal efficiency is presented in Figure 6(a). It exhibits that the removal efficiency increases with decreasing initial Cr(VI) concentration and increasing S-nZVI@H dose. S-nZVI@H can provide more surface-active sites improving the reduction ability of Cr(VI). The higher the initial concentration of Cr (VI), the more surface-active sites of S-nZVI can be occupied, resulting the lower removal efficiency of Cr(VI) (Khosravi & Arabi 2016). At S-nZVI@H dose 7.72 g/L and initial Cr(VI) concentration 10.10 mg/L, a maximum Cr(VI) removal of 91.36% is determined.
The reciprocal effect of contact time and S-nZVI@H dose on Cr(VI) removal efficiency is shown in Figure 6(b). As S-nZVI@H dose and contact time increases, the removal efficiency of Cr(VI) improves. The removal efficiency of Cr(VI) increases rapidly at the initial contact time, which indicates that the reduction of Cr(VI) is predominant (Ponder et al. 2000). However, with the further extension of contact time, the Cr(VI) removal efficiency increases slowly, which is due to the accumulation of Fe(III)-Cr(III) hydroxides on the surface of S-nZVI@H hindering the reaction between Cr(VI) and S-nZVI (Wu et al. 2015;Li et al. 2017c). In addition, it can be clearly observed that the curvature of the surface is relatively large, which indicates that the interaction of contact time and S-nZVI@H dose has a great influence on the Cr(VI) removal efficiency. A maximum Cr(VI) removal (98.95%) is observed at S-nZVI@H dose of 8.76 g/L and contact time of 39.57 min.
Figure 6(c) shows the combined effect of initial Cr(VI) concentration and contact time on removal of Cr(VI). With the increase of contact time and the decrease of initial Cr(VI) concentration, the removal efficiency of Cr(VI) increases continuously. The extended contact time provides sufficient reaction time for the reduction and adsorption of Cr(VI) by S-nZVI@H. Under the condition of higher initial Cr(VI) concentration, the removal efficiency of Cr(VI) is reduced. This can be attributed to the limited number of active sites provided by a fixed amount of S-nZVI@H. At initial Cr(VI) concentration 10.02 mg/L and contact time 36.39 min, a maximum Cr(VI) removal of 93.63% is determined.
The plot for interactive effect of S-nZVI@H dose and initial pH (Figure 6(d)) shows that increasing initial pH results in a decreasing removal of Cr(VI), conversely, it increases with the enhance of S-nZVI@H dose. This is because, under alkaline conditions, nZVI appears electronegative; under acidic conditions, nZVI appears electrically positive (Gong et al. 2017). Cr(VI) exists mainly in the form of HCrO À 4 in acidic conditions, and only in the form of CrO 2À 4 in alkaline solutions (Lv et al. 2011). Obviously, in alkaline solution, negatively charged nZVI and CrO 2À 4 are more likely to generate electrostatic repulsion, which inhibits their interaction leading to the decrease of Cr(VI) removal. A maximum Cr(VI) removal (90.33%) is determined at S-nZVI@H dose 8.30 g/L and initial pH 5.3.
The interactive influence of initial Cr(VI) concentration and initial pH on Cr(VI) removal is shown in Figure 6(e). Under the dual function of high pH value and high initial Cr(VI) concentration, the removal efficiency of Cr(VI) is reduced. Moreover, it can be observed that the curvature of the response surface is small, which indicates that the interaction between initial Cr(VI) concentration and initial pH has slightly influence on the removal efficiency of Cr(VI). At Initial Cr(VI) concentration 10.07 mg/L and initial pH 3.72, a maximum Cr(VI) removal of 87.72% is determined.
The interaction of contact time and initial pH on Cr(VI) removal is shown in Figure 6(f). It may be noted that the trend of Cr(VI) removal efficiency is consistent with the change of contact time and is contrary to the initial pH. Similarly, the contact time and the initial pH play the same role as stated above. A maximum Cr(VI) removal (89.8%) is determined at contact time of 37.61 min and initial pH of 5.38.

Model validation
As an optimization technology, RSM needs to be verified for its adaptability (Bezerra et al. 2008). In order to evaluate the validity and feasibility of the RSM model, three parallel experiments were carried out under the conditions of independent variables corresponding to the maximum Cr(VI) removal efficiency determined by the model (Table 4). The predicted Uncorrected Proof optimum removal conditions obtained from RSM: S-nZVI@H dose (9.46 g/L), initial Cr(VI) concentration (30 mg/L), contact time (40.7 min) and initial pH (5.27). The relative error of prediction between the mean value of the experimental (97.75%) and predicted (99.76%) removal efficiency was calculated as a result of 2.07%, which showed that the quadratic polynomial model can well predict the removal of Cr(VI) by S-nZVI@H (Ashrafi et al. 2018).

CONCLUSIONS
In this study, two materials of nZVI@H and S-nZVI@H are successfully synthesized for Cr(VI) removal. With the better removal effects confirmed by SEM and FTIR characterizations and comparable experiments, S-nZVI@H is selected as the material designed by RSM to further explore its removal efficiency of Cr(VI). Furthermore, BBD experimental design is used to reveal the influence of the interaction of four independent variables on the Cr(VI) removal efficiency and the predicted optimum removal conditions are determined to be as follows: S-nZVI@H dose 9.46 g/L, initial Cr(VI) concentration 30 mg/L, contact time 40.7 min and initial pH 5.27. Additionally, the S-nZVI@H dose is the key factor affecting the removal of Cr(VI). The variance analysis and residual analysis of the experimental data are carried out by the quadratic polynomial model. The analysis results show that the correlation between the experimental values and the predicted values is high (F ¼ 118.73, P , 0.0001, R 2 ¼ 0.9916), which corroborates the quality and reliability of the model. In order to verify the validity and feasibility of the model, three parallel experiments are carried out under the predicted optimum removal conditions. The removal efficiency of S-nZVI@H for Cr(VI) obtained from the experiment (97.75%) is very close to the predicted value of the model (99.76%). In conclusion, BBD based on RSM can be used to statistically optimize the experimental study of Cr(VI) removal by S-nZVI@H.